发表机构
The Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对在线零售中删失需求下的情境定价与库存学习问题，提出Mean-Calibrated Kernel UCB算法，证明其极小极大最优性并通过实验验证有效性。
AI 中文摘要
在在线零售中，当产品售罄时，零售商通常只能看到已售出的单位数量，而无法得知若有库存可用时会有多少顾客购买。然而，库存水平决定了会揭示多少需求，这些信息会影响后续决策和未来利润。我们研究了一个在线销售问题，在每一轮中，卖家观察市场情境，然后根据前几轮的删失销售数据做出定价和库存决策。挑战在于学习一种依赖情境的定价和库存策略，而无需假设需求的特定公式，也无需观察已实现的利润。为克服这一困难，我们提出了Mean-Calibrated Kernel UCB（MCK-UCB）算法，该算法利用过去几轮相似市场情境的数据，将每个不完整的销售记录转化为对库存和价格决策的可靠指导。这种设计使我们能够在服务顾客的同时进行学习，无需单独的探索阶段，也无需恢复因缺货而隐藏的所有需求。我们证明了所提出算法的极小极大最优性，当期望利润随价格变化更平滑时，其收敛速度明显更快。我们还进行了全面的数值实验，以验证所提算法的有效性。
英文摘要
In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.
Comments31 pages, 3 figures
